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Differentiates a circuit using Central Differencing.
Inherits From: LinearCombination
, Differentiator
tfq.differentiators.CentralDifference(
error_order=2, grid_spacing=0.001
)
Central differencing computes a derivative at point x using an equal number of points before and after x. A closed form for the coefficients of this derivative for an arbitrary positive error order is used here, which is described in the following article: https://www.sciencedirect.com/science/article/pii/S0377042799000886
my_op = tfq.get_expectation_op()
linear_differentiator = tfq.differentiators.CentralDifference(2, 0.01)
# Get an expectation op, with this differentiator attached.
op = linear_differentiator.generate_differentiable_op(
analytic_op=my_op
)
qubit = cirq.GridQubit(0, 0)
circuit = tfq.convert_to_tensor([
cirq.Circuit(cirq.X(qubit) ** sympy.Symbol('alpha'))
])
psums = tfq.convert_to_tensor([[cirq.Z(qubit)]])
symbol_values_array = np.array([[0.123]], dtype=np.float32)
# Calculate tfq gradient.
symbol_values_tensor = tf.convert_to_tensor(symbol_values_array)
with tf.GradientTape() as g:
g.watch(symbol_values_tensor)
expectations = op(circuit, ['alpha'], symbol_values_tensor, psums)
# Gradient would be: 50 * f(x + 0.02) + 200 * f(x + 0.01)  150 * f(x)
grads = g.gradient(expectations, symbol_values_tensor)
grads
tf.Tensor([[1.1837807]], shape=(1, 1), dtype=float32)
Args  

error_order

A positive, even int specifying the error order
of this differentiator. This corresponds to the smallest power
of grid_spacing remaining in the series that was truncated
to generate this finite differencing expression.

grid_spacing

A positive float specifying how large of a
grid to use in calculating this finite difference.

Methods
differentiate_analytic
@tf.function
differentiate_analytic( programs, symbol_names, symbol_values, pauli_sums, forward_pass_vals, grad )
Differentiate a circuit with analytical expectation.
This is called at graph runtime by TensorFlow. differentiate_analytic
calls he inheriting differentiator's get_gradient_circuits
and uses
those components to construct the gradient.
Args  

programs

tf.Tensor of strings with shape [batch_size] containing
the string representations of the circuits to be executed.

symbol_names

tf.Tensor of strings with shape [n_params], which
is used to specify the order in which the values in
symbol_values should be placed inside of the circuits in
programs .

symbol_values

tf.Tensor of real numbers with shape
[batch_size, n_params] specifying parameter values to resolve
into the circuits specified by programs, following the ordering
dictated by symbol_names .

pauli_sums

tf.Tensor of strings with shape [batch_size, n_ops]
containing the string representation of the operators that will
be used on all of the circuits in the expectation calculations.

forward_pass_vals

tf.Tensor of real numbers with shape
[batch_size, n_ops] containing the output of the forward pass
through the op you are differentiating.

grad

tf.Tensor of real numbers with shape [batch_size, n_ops]
representing the gradient backpropagated to the output of the
op you are differentiating through.

Returns  

A tf.Tensor with the same shape as symbol_values representing
the gradient backpropageted to the symbol_values input of the op
you are differentiating through.

differentiate_sampled
@tf.function
differentiate_sampled( programs, symbol_names, symbol_values, pauli_sums, num_samples, forward_pass_vals, grad )
Differentiate a circuit with sampled expectation.
This is called at graph runtime by TensorFlow. differentiate_sampled
calls he inheriting differentiator's get_gradient_circuits
and uses
those components to construct the gradient.
Args  

programs

tf.Tensor of strings with shape [batch_size] containing
the string representations of the circuits to be executed.

symbol_names

tf.Tensor of strings with shape [n_params], which
is used to specify the order in which the values in
symbol_values should be placed inside of the circuits in
programs .

symbol_values

tf.Tensor of real numbers with shape
[batch_size, n_params] specifying parameter values to resolve
into the circuits specified by programs, following the ordering
dictated by symbol_names .

pauli_sums

tf.Tensor of strings with shape [batch_size, n_ops]
containing the string representation of the operators that will
be used on all of the circuits in the expectation calculations.

num_samples

tf.Tensor of positive integers representing the
number of samples per term in each term of pauli_sums used
during the forward pass.

forward_pass_vals

tf.Tensor of real numbers with shape
[batch_size, n_ops] containing the output of the forward pass
through the op you are differentiating.

grad

tf.Tensor of real numbers with shape [batch_size, n_ops]
representing the gradient backpropagated to the output of the
op you are differentiating through.

Returns  

A tf.Tensor with the same shape as symbol_values representing
the gradient backpropageted to the symbol_values input of the op
you are differentiating through.

generate_differentiable_op
generate_differentiable_op(
*, sampled_op=None, analytic_op=None
)
Generate a differentiable op by attaching self to an op.
This function returns a tf.function
that passes values through to
forward_op
during the forward pass and this differentiator (self
) to
backpropagate through the op during the backward pass. If sampled_op
is provided the differentiators differentiate_sampled
method will
be invoked (which requires sampled_op to be a sample based expectation
op with num_samples input tensor). If analytic_op is provided the
differentiators differentiate_analytic
method will be invoked (which
requires analytic_op to be an analytic based expectation op that does
NOT have num_samples as an input). If both sampled_op and analytic_op
are provided an exception will be raised.
This generate_differentiable_op()
can be called only ONCE because
of the one differentiator per op
policy. You need to call refresh()
to reuse this differentiator with another op.
Args  

sampled_op

A callable op that you want to make differentiable
using this differentiator's differentiate_sampled method.

analytic_op

A callable op that you want to make differentiable
using this differentiators differentiate_analytic method.

Returns  

A callable op that who's gradients are now registered to be
a call to this differentiators differentiate_* function.

get_gradient_circuits
@tf.function
get_gradient_circuits( programs, symbol_names, symbol_values )
See base class description.
refresh
refresh()
Refresh this differentiator in order to use it with other ops.